13. K modeling

13.1. Characteristics of modeling

We use the same ingredients as the J modeling by combining ALGO_CONT = STANDARD for zone 1 with GLISSIERE with ALGO_CONT = PENALISATION for zone 2.

3D modeling (linear elements) is used.

The continuous contact formulation is used. This test case is used to validate the CONTACT_INIT = “INTERPENETRE” feature. Here we use the GLISSIERE function, which makes it possible to maintain contact throughout the extrusion, mathematically. The result is physically similar to modeling without a slide, since it is a frictionless extrusion.

13.2. Characteristics of the mesh

Number of knots: 3292

Number of meshes: 2150 HEXA8, 260 PENTA6, 260, 1814 QUAD4 and 68 TRIA63

Number of nodes in contact: 210

13.3. Tested sizes and results

The reference values are considered to be those of modeling C. The following displacement \(Y\) of the point \(K\) of the plot with respect to the surface \(\mathrm{ABCDEFG}\) of the die is tested.

Identification	Reference type	Reference value	Tolerance
Point \(K\)/Point \(B\) - \(\mathrm{DY}\)	“ANALYTIQUE”	5.0000	0.10%
Point \(K\)/Point \(C\) - \(\mathit{DY}\)	“ANALYTIQUE”	20.8250	2.0%
Point \(K\)/Point \(D\) - \(\mathit{DY}\)	“ANALYTIQUE”	55.8800	1.50%
Point \(K\)/Point \(E\) - \(\mathit{DY}\)	“ANALYTIQUE”	140.0	0.2%	0, 2%
Point \(K\)/Point \(F\) - \(\mathit{DY}\)	“ANALYTIQUE”	155.0	0.2%

We test the number of iterations of Newton when the point \(K\) of the plot is in front of the points \(B\), \(C\), \(D\), \(E\) and \(F\) of the chain.

Identification	Reference type	Reference value	Tolerance
ITER_GLOB/Point \(B\)	“NON_REGRESSION”	1	0.00%
ITER_GLOB/Point \(C\)	“NON_REGRESSION”	1	0.00%
ITER_GLOB/Point \(D\)	“NON_REGRESSION”	1	0.00%
ITER_GLOB/Point \(E\)	“NON_REGRESSION”	1	0.00%
ITER_GLOB/Point \(F\)	“NON_REGRESSION”	1	0.00%

13.4. notes

The calculation is carried out by imposing a displacement on the back side of the block \(\text{(MN)}\). The displacement is imposed in the following way:

from	\(0\mathit{mm}\) to	\(20\mathit{mm}\) in 4 steps
from	\(20\mathit{mm}\) to	\(70\mathit{mm}\) in 5 steps
from	\(70\mathit{mm}\) to	\(140\mathit{mm}\) in 2 steps
from	\(140\mathit{mm}\) to	\(155\mathit{mm}\) in 1 step

In this modeling, the external forces are sufficiently important and the use of an absolute convergence criterion is not mandatory because the symmetry conditions on the plot have been slightly disturbed.